|
|
A269226
|
|
Period 6: repeat [3, 9, 6, 6, 9, 3].
|
|
1
|
|
|
3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The palindromic sequence arising when the digital root of n alternates diagonally in opposite directions on a square grid. This is the sequence of 3-6-9 appearing every third column on a square grid when A010888 (digital root of n) alternates in both directions diagonally. Other columns are the digital root of 2^n: {1, 2, 4, 8, 7, 5}, or in its opposite direction 5^n: {5,7,8,4,2,1}. All diagonals parallel to the digital roots of n are also {1,2,3,4,5,6,7,8,9} or {9,8,7,6,5,4,3,2,1}.
See the link below for a visual illustration.
This sequence also arises when A180592 (digital root of 2n) is substituted for A010888.
|
|
LINKS
|
|
|
FORMULA
|
a(n+1) = digital root of 5^n - 2^n.
a(n) = (12 - 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 3*sqrt(3)*sin(2*n*Pi/3))/2. - Wesley Ivan Hurt, Oct 05 2018
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|